A182373 Positive integers k such that k*3^k - 2 is prime.

3, 5, 7, 37, 45, 53, 179, 277, 721, 2087, 6197, 6317, 8775, 12781, 38943, 47273, 50507, 66693

Offset: 1

Author

Patrick Devlin, Apr 26 2012

Keywords

• nonn
• more

Comments

Similar to A060353, and to the Woodall primes, A050918. The next term in the sequence is unknown; if the sequence is infinite, the next term is greater than 5000.

a(15) > 30000. - Tyler NeSmith, Apr 22 2022

a(19) > 10^5. - Michael S. Branicky, Sep 22 2024

Examples

			79 = 3*3^3 - 2; 1213 = 5*3^5 - 2; 15307 = 7*3^7 - 2.
		

Crossrefs

Cf. A050918, A060353.

Programs

Maple

#choose N large, then S is the desired set
f:=n->n*3^n - 2:
S:={}:
for n from 0 to N do if(isprime(f(n))) then S:=S union {n}: fi: od

Mathematica

Select[Range[2100], PrimeQ[#*3^# - 2] &] (* Jayanta Basu, Jun 01 2013 *)

PARI

for(n=1, 1e6, if(ispseudoprime(3^n*n - 2), print1(n, ", "))) \\ Altug Alkan, Dec 01 2015

Extensions

a(11)-a(14) from Altug Alkan, Dec 01 2015

a(15)-a(17) from Michael S. Branicky, Apr 23 2023

a(18) from Michael S. Branicky, Sep 22 2024